Efraim Armendariz (efraim@math.utexas.edu): Research interests include the general structure theory of noncommucative rings and their modules, with an emphasis on rings satisfying a polynomial identity and von Neumann regular rings; radical properties and torsion theories for ring and module categories. Professional interests include issues in mathematics education and reform mechanisms which lead to improved access for groups not traditionally represented in the mathematical sciences.
John Durbin (durbin@math.utexas.edu): Research interests include Groups.
Frank Gerth III (gerth@math.utexas.edu): Research interests include Algebraic Number Theory, including class numbers, class groups, discriminants, class field theory, density theorems, Iwasawa theory.
Raymond Heitmann (heitmann@math.utexas.edu): Research interests include Algebra and Commutative Rings.
Sean M. Keel (keel@math.utexas.edu): Research interests include Algebraic Geometry, particularly Mori's program, GIT, moduli problems, and intersection theory.
Stephen McAdam (mcadam@math.utexas.edu): Research interests include commutative rings. His future research plans are to continue developing the theory of asymptotic and essential prime divisors and their applications, and to study projective equivalence.
Alan W. Reid (areid@math.utexas.edu): Research interests include low-dimensional topology and discrete groups. He is particularly interested in the geometry and topology of hyperbolic 3-manifolds, and properties of their fundamental groups. He is also interested in connections between hyperbolic 3-manifolds and number theory..
Fernando Rodríguez Villegas (villegas@math.utexas.edu): Research interests include special values of L-functions (Birch-Swinnerton-Dyer and Bloch-Beilinson conjectures), arithmetic of elliptic curves, modular forms, Mahler measure of polynomials.
David Saltman (saltman@math.utexas.edu): Research interests include Brauer group theory and division algebras, with an emphasis on invariant theory of groups acting on fields, rationality of invariant fields, the center of the generic division algebra, and division algebras over p-adic curves and their geometry.
Martha Smith (mks@math.utexas.edu): Research interests include Ring Theory, geometry, statistics, and teacher preparation.
John Tate (tate@math.utexas.edu): Research interests include Algebraic Number Theory (local and global fields), Class Field Theory, Galois cohomology, Galois representations, L-functions and their special values, modular forms, elliptic curves and abelian varieties.
Jeffrey Vaaler (vaaler@math.utexas.edu): Research interests include Analytic Number Theory, Diophantine approximation and the geometry of numbers in local and global fields, Diophantine inequalities, polynomials, effective measures of irrationality and transcendence, applications of Fourier analysis in number theory, inequalities and extremal problems.
Felipe Voloch
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):
Research interests include arithmetic of function fields. Diophantine
geometry over function fields. Geometry of algebraic curves. Arithmetic
analogues of geometric methods. Modular forms, elliptic curves and
abelian varieties. Applications to coding theory.